Local exchange-correlation vector potential with memory in time-dependent density functional theory: The generalized hydrodynamics approach

Using Landau Fermi-liquid theory we derive a nonlinear nonadiabatic approximation for the exchange-correlation (xc) vector potential defined by the xc stress tensor. The stress tensor is a local nonlinear functional of two basic variables: the displacement vector and the second-rank tensor which describes the evolution of momentum in a local frame moving with Eulerian velocity. For irrotational motion and the equilibrium initial state the dependence on the tensor variable reduces to that on the metrics generated by dynamical deformation of the system.